Explaining Measurement Nonequivalence Using Multilevel Structural Equation Modeling

It is necessary to test for equivalence of measurements across groups to guarantee that comparisons of regression coefficients or mean scores of a latent factor are meaningful. Unfortunately, when tested, many scales display nonequivalence. Several researchers have suggested that nonequivalence may be used as a useful source of information as to why equivalence is biased and proposed employing a multilevel structural equation modeling (MLSEM) approach to explain why equivalence is not given. This method can consider a latent between-level factor and/or single contextual variables and use them to explain items’ nonequivalence. In the current study, we show that this method may also be useful for social science studies in general and for survey research and sociological comparative studies in particular when one fails to establish cross-group equivalence. We utilize data from the International Social Survey Program national identity module (2003) to test for the cross-country equivalence of a scale measuring attitudes toward granting citizenship rights to immigrants. As expected, the scale fails to achieve scalar equivalence. However, we explain a significant part of the most nonequivalent intercept by a latent between-level factor and one contextual variable, namely, the percentage of foreigners in the country relying on group threat theory. We show that the method does not necessarily rectify nonequivalence, but it can help to explain why it is absent.